Mechatronics and Electrical Drives

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Fachgebiet eistungselektronik und Elektrische Antriebstechnik Prof. Dr. Ing. Joachim Böcker Mechatronics and Electrical Drives 29.02.

1 Fachgebiet eistungselektronik und Elektrische Antriebstechnik Prof. Dr. Ing. Joachim Böcker Mechatronics and Electrical Drives Surname: Student number: First name: Course of Study: Task: (Points) 1 (20) 2 (17) 3 (17) Total (54) Grade Duration: 120 Minutes Permitted: a non-programmable calculator without graphic display drawing materials (compasses, protractor, ruler, pens...) Please note: Please prepare your student ID card (with photo) on your desk for the attendance check. Please label each exam sheet with your name and student number. Use a new exam sheet for each task. Do not use pencils or red pens. With numerical calculations, the units must be considered in every step. Not following that rule will result in deduction of points. All solutions must be clearly documented and wherever required explained! The entry of a mere final result without any approach will not be counted. You can only take part in the exam, if you are registered in the PAU system. If you take part without registration, the exam result will not be considered. Good uck! Exam Mechatronics and electrical drives WS 2015 / 2016 Page 1 of 9

2 Fachgebiet eistungselektronik und Elektrische Antriebstechnik Task 1: Magnetic Bearing (20 Points) Shown below are two iron sections with different cross sectional areas a shaft in-between. The upper and lower cores are provided with windings of turns each and are excited with the currents and respectively. The shaft between both iron sections has a gravitational force and a distance of to the upper and lower yoke. and In the following the behavior of the iron can be idealized I 1 r i,1 A Fe1 r o A Fe1 d d A Fe2 F g A Fe2 x r o r i,2 y I Calculate the resulting force on the shaft if the excitation is and. (3 P) 1.2 Calculate the current to compensate for the gravitational force of the shaft. The current is still. (6 P) 1.3 What is the need of a bias current in a magnetic bearing? Please explain your answer. (3 P) The magnetic bearing should be supplied via a four-quadrant converter with pulse-width modulation. 1.4 Sketch the schematic of a four-quadrant converter for one winding. (2 P) 1.5 The DC link voltage is. The requested voltage is. Sketch the corresponding profiles (switching commands and output voltage) in the diagram given below. The carrier signals are indicated above. Make sure to complete the axis labels. (6 P) Exam Mechatronics and electrical drives WS 2015 / 2016 Page 2 of 9

3 Fachgebiet eistungselektronik und Elektrische Antriebstechnik c 1 (t) t c 2 (t) s 1 (t) T s 2T s 3T s 4T s t s 2 (t) t u(t) t Exam Mechatronics and electrical drives WS 2015 / 2016 Page 3 of 9

4 Fachgebiet eistungselektronik und Elektrische Antriebstechnik Task 2: Switched Reluctance Motor (17 Points) 2.1 Given are the following 2/2 switched reluctance motors with different rotor pole areas. In the first case the rotor pole area is equal to the stator pole area. In the second case the rotor pole area is smaller than the stator pole area. Please assign the correct inductance profiles to the two switched reluctance motor cases.(3 P) a) b) c) d) e) f) g) h) i) j) Exam Mechatronics and electrical drives WS 2015 / 2016 Page 4 of 9

Fachgebiet eistungselektronik und Elektrische Antriebstechnik The following figures illustrate the mechanical work for one electrical cycle and different (low, medium and high) speeds. 2.

5 Fachgebiet eistungselektronik und Elektrische Antriebstechnik The following figures illustrate the mechanical work for one electrical cycle and different (low, medium and high) speeds. 2.2 Please describe in detail why the mechanical work decreases when the rotor speed increases. (4 P) Given is the magnetization characteristics of a switched reluctance motor with one pole pair for the positions and. The maximum current is. The electrical and mechanical losses can be considered to be negligible. ψ in Vs 2,2 2,0 = 0 1,0 = π/ i in A 2.3 Calculate the mechanical work, and the peak value of the electrical work fed into the motor for one electrical period. (2 P) 2.4 Calculate the mean torque of one electrical period. (2 P) 2.5 Sketch qualitatively the trajectories of current, voltage and inductance over the time of one electrical period. Consider the speed of the motor as low and the stator pole area as. (6 P) The processes of magnetization and demagnetization have to be considered. No calculations are necessary. Use the diagram given below and make sure to complete axis labels Exam Mechatronics and electrical drives WS 2015 / 2016 Page 5 of 9

6 Fachgebiet eistungselektronik und Elektrische Antriebstechnik i u Exam Mechatronics and electrical drives WS 2015 / 2016 Page 6 of 9

7 Fachgebiet eistungselektronik und Elektrische Antriebstechnik Task 3: BDC Motor (17 Points) Consider a symmetrical 3-phase BDC Motor operating at = 1000 min -1. The injected block-shaped current and the line-line back EMF is shown in the next page. 3.1 Calculate the following: a) The mechanical power delivered to the load. (1P) b) The torque developed by the motor. (1P) c) Sketch the variation of the induced phase EMFs, and (in the next page). Indicate the appropriate values. (4P) d) Sketch the corresponding block shaped currents and (in the next sheet). Indicate the appropriate values. (2P) 3.2 The motor is fed by a three phase inverter as shown below:... u dc S1 S2 S3 S4 S5 S6 i a i b i c R R R M M M e a e b e c. Consider the instant 210º, refer next page, when the commutation is about to begin. a) Define the differential equation defining the commutation. (2P) b) Calculate the commutation time. Assume, (1P) Exam Mechatronics and electrical drives WS 2015 / 2016 Page 7 of 9

8 Fachgebiet eistungselektronik und Elektrische Antriebstechnik i c 10A A 200V e ca -200V e a e b e c i a i b Exam Mechatronics and electrical drives WS 2015 / 2016 Page 8 of 9

9 Fachgebiet eistungselektronik und Elektrische Antriebstechnik 3.3 The simplified control structure for the speed control of the BDC motor is shown in the figure below. The simplified plant transfer function represents the dynamic behavior from torque demand to angular speed. includes the current controlled electrical subsystem and inertia. A load torque is not considered in the control loop. (These details are given to understand the background, however, they are not necessary to solve the following tasks.). The given plant data are, and. The speed controller transfer function is, ω ref + - G c (s) T ref G s (s) ω If the controller is assumed as PI-type and is designed using symmetric optimum method, obtain the following: a) The open-loop and closed loop transfer function (2 P) b) The controller reset time if the desired crossover frequency is. (2 P) c) Magnitude of the controller gain (2 P) Exam Mechatronics and electrical drives WS 2015 / 2016 Page 9 of 9

Synchronous Motor Drives

UNIT V SYNCHRONOUS MOTOR DRIVES 5.1 Introduction Synchronous motor is an AC motor which rotates at synchronous speed at all loads. Construction of the stator of synchronous motor is similar to the stator